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Logic and Algebra in Unfolded Petri Nets : on a Duality Between Concurrency and Causal Dependence

Bernardinello Luca, Ferigato Carlo, Pomello Lucia

Fundamenta Informaticae

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2020

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Vol. 171, nr 1-4

39--56

EN

An orthogonality space is a set endowed with a symmetric and irreflexive binary relation (an orthogonality relation). In a partially ordered set modelling a concurrent process, two such binary relations can be defined: a causal dependence relation and a concurrency relation, and two distinct orthogonality spaces are consequently obtained. When the condition of N-density holds on both these orthogonality spaces, we study the orthomodular poset formed by closed sets defined according to Dacey. We show that the condition originally imposed by Dacey on the orthogonality spaces for obtaining an orthomodular poset from his closed sets is in fact equivalent to N-density. The requirement of N-density was as well fundamental in a previous work on orthogonality spaces with the concurrency relation. Starting from a partially ordered set modelling a concurrent process, we obtain dual results for orthogonality spaces with the causal dependence relation in respect to orthogonality spaces with the concurrency relation.

2

A modiﬁed independent component analysis-based fault detection method in plant-wide systems

Teimoortashloo M., Sedigh A. K.

Control and Cybernetics

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2015

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Vol. 44, no. 2

287--310

EN

This paper presents a modiﬁed Independent Component Analysis (ICA)-based Fault Detection Method (FDM). The proposed FDM constructs a set of matrices, revealingthe trend of the variable samples and execute ICA algorithm for each set of matrices in contrast to the FDM based on dynamic ICA (DICA) which constructs the high dimensional augmented matrix. This paper shows that the proposed FDM decreases the matrix dimensions and as a result compensates for some disadvantages of using the high dimensional matrix discussed in previous articles. Furthermore, other advantages of the proposed FDM are the decreases in the running time, computational cost of the algorithm and the orthogonalization estimation errors. Moreover, the proposed method improves the detectability for a class of faults compared to DICA-based FDM. This class of fault occurs when two or more consecutive samples of fault source signal have opposite signs and cancel out each other. Simulation results are provided to show the eﬀectiveness of the proposed methodology.

3

Comparisons of prewhitening algorithms of noisy signals

Cichocki A., Osowski S., Siwek K.

Przegląd Elektrotechniczny

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2005

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R. 81, nr 2

22-25

EN

The paper presents and compares the performance of different prewhitening algorithms of the signals in the presence of white noise. The algorithms have been applied to the decorrelation of the statistically dependent and independent signals mixed together. The presented technigue may find application in the solutions of the blind source separation problems.

PL

Artykuł przedstawia i porównuje działanie różnych algorytmów wybielania sygnałów w obecności białego szumu. Badane algorytmy zastosowano do dekorelacji zależnych i niezależnych sygnałów zmieszanych w nieznany sposób. Proponowane rozwiązanie znajduje zastosowanie jako wstępny etap ślepej separacji sygnałów.